
from __future__ import annotations

from decimal import Decimal
from math import *  # noqa: F403

from sympy import diff




def       _SCREAMING_SNAKE_CASE   (						_lowerCamelCase					:     str		,    _lowerCamelCase					:     float | Decimal		,    _lowerCamelCase					:     float = 10**-10)   ->       float:






							'''simple docstring'''





							__UpperCamelCase      :  Tuple       =   a
							while True:
														__UpperCamelCase      :  int       =   Decimal(_lowerCamelCase) - (
														    Decimal(eval(_lowerCamelCase)) / Decimal(eval(str(diff(_lowerCamelCase))))  # noqa: S307
														)
														# This number dictates the accuracy of the answer
														if abs(eval(_lowerCamelCase)) < precision:  # noqa: S307
																					return float(_lowerCamelCase)


# Let's Execute
if __name__ == "__main__":
		# Find root of trigonometric function
		# Find value of pi
		print(f"The root of sin(x) = 0 is {newton_raphson('sin(x)', 2)}")
		# Find root of polynomial
		print(f"The root of x**2 - 5*x + 2 = 0 is {newton_raphson('x**2 - 5*x + 2', 0.4)}")
		# Find Square Root of 5
		print(f"The root of log(x) - 1 = 0 is {newton_raphson('log(x) - 1', 2)}")
		# Exponential Roots
		print(f"The root of exp(x) - 1 = 0 is {newton_raphson('exp(x) - 1', 0)}")

from __future__ import annotations

from math import pi
from typing import Protocol

import matplotlib.pyplot as plt
import numpy as np




class 					lowerCamelCase__				(							__lowercase):




	'''simple docstring'''




	def   _lowerCamelCase							(   self						:Tuple	,  a						:float		)						->					float:
								return 0.0




def       _SCREAMING_SNAKE_CASE   (						_lowerCamelCase					:     np.ndarray		,    _lowerCamelCase					:     int)   ->       tuple[int | float, int | float]:






							'''simple docstring'''





							__UpperCamelCase      :  List[str]       =   min([-20, np.min(fft_results[1 : samplerate // 2 - 1])])
							__UpperCamelCase      :  Any       =   max([20, np.max(fft_results[1 : samplerate // 2 - 1])])
							return lowest, highest




def       _SCREAMING_SNAKE_CASE   (						_lowerCamelCase					:     FilterType		,    _lowerCamelCase					:     int)   ->       None:






							'''simple docstring'''





							__UpperCamelCase      :  List[str]       =   512
							__UpperCamelCase      :  List[Any]       =   [1] + [0] * (size - 1)
							__UpperCamelCase      :  List[Any]       =   [filter_type.process(_lowerCamelCase) for item in inputs]

							__UpperCamelCase      :  Optional[Any]       =   [0] * (samplerate - size)  # zero-padding
							outputs += filler
							__UpperCamelCase      :  Optional[int]       =   np.abs(np.fft.fft(_lowerCamelCase))
							__UpperCamelCase      :  Optional[int]       =   20 * np.logaa(_lowerCamelCase)

							# Frequencies on log scale from 24 to nyquist frequency
							plt.xlim(24		,    samplerate / 2 - 1)
							plt.xlabel("Frequency (Hz)")
							plt.xscale("log")

							# Display within reasonable bounds
							__UpperCamelCase      :  Optional[Any]       =   get_bounds(_lowerCamelCase		,    _lowerCamelCase)
							plt.ylim(max([-80, bounds[0]])		,    min([80, bounds[1]]))
							plt.ylabel("Gain (dB)")

							plt.plot(_lowerCamelCase)
							plt.show()




def       _SCREAMING_SNAKE_CASE   (						_lowerCamelCase					:     FilterType		,    _lowerCamelCase					:     int)   ->       None:






							'''simple docstring'''





							__UpperCamelCase      :  Any       =   512
							__UpperCamelCase      :  Dict       =   [1] + [0] * (size - 1)
							__UpperCamelCase      :  Tuple       =   [filter_type.process(_lowerCamelCase) for item in inputs]

							__UpperCamelCase      :  Dict       =   [0] * (samplerate - size)  # zero-padding
							outputs += filler
							__UpperCamelCase      :  Optional[int]       =   np.angle(np.fft.fft(_lowerCamelCase))

							# Frequencies on log scale from 24 to nyquist frequency
							plt.xlim(24		,    samplerate / 2 - 1)
							plt.xlabel("Frequency (Hz)")
							plt.xscale("log")

							plt.ylim(-2 * pi		,    2 * pi)
							plt.ylabel("Phase shift (Radians)")
							plt.plot(np.unwrap(_lowerCamelCase		,    -2 * pi))
							plt.show()